They were filming at night when it's 40s/50s, so bare shoulders are going to be cold.
You can see on a lot of indoor sets, too, that between takes the actors are bundled in coats because the AC is blasting so they don't sweat on camera unless they're supposed to.
I noticed they're shooting on Hollywood Blvd, around some pretty recognizable landmarks. Of course, these may not be in the shoot, but any word on where this is supposed to take place?